Perceptual discrimination has been explained as the outcome of a stochastic evidence accumulation process. Stop-signal task performance has been explained as the outcome of a race between a GO and a STOP process. We seek to integrate these two modeling frameworks. Macaques and humans performed a visual saccadic choice RT stop-signal task. The choice stimulus was a cyan-magenta checkerboard that appeared above a central fixation spot. Saccade choice was specified by the fraction of cyan or magenta in the checkerboard, varied around discrimination threshold. On 25-40% of trials a visual stop signal replaced the central fixation spot after a variable stop-signal delay. Monkeys were reinforced on no-stop signal trials for correct choices and on stop signal trials for inhibiting the saccade. Behavioral results demonstrate that STOP process duration (stop signal reaction time) did not vary with choice difficulty indicating that perceptual choice and response inhibition function independently (Middlebrooks & Schall 2013 AP&P). Here, we describe an interactive stochastic accumulator model to explain performance of choice and stopping as a function of perceptual choice difficulty. The model assumes one stochastic accumulator for each response alternative plus one accumulator for the stop process (interrupting the response accumulators). Each accumulator has a threshold, an accumulation rate, and a non-decision time. We consider three mechanisms of choice (race, feed-forward inhibition, and lateral inhibition) and three accounts of the manipulation of choice performance (rate, threshold, non-decision time). We fit the various model architectures to the data to determine their account of performance across choice difficulty and stop-signal delays. Each choice mechanism accounted for performance, but best fits used lateral inhibition mechanisms. Variation in accumulation rate provided the best account of variation in choice difficulty. This finding provides a framework in which to interpret patterns of modulation in the neural circuits mediating performance of this task.